Magnetic Effects of Electric Current - Field due to a current carrying conductor

Hans Christian Oersted discovered that an electric current flowing through a metallic conductor produces a magnetic field around it.

The magnetic field lines around a straight current-carrying conductor are concentric circles whose centers lie on the wire. The direction of these field lines is given by the Right-Hand Thumb Rule.

Right-Hand Thumb Rule: Imagine holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of current ($I$); then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field ($B$).

The magnitude of the magnetic field ($B$) produced by a straight wire at a given point is directly proportional to the current ($I$) passing through the wire and inversely proportional to the distance ($r$) from the wire: $B \propto \frac{I}{r}$.

For a circular loop, the magnetic field lines are nearly circular near the wire but appear as straight lines at the center of the loop. The magnetic field produced by a coil of $n$ turns is $n$ times as large as that produced by a single turn, because the current in each circular turn has the same direction and the fields then just add up.

A solenoid is a coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder. The magnetic field pattern inside a solenoid is uniform and consists of parallel straight lines, indicating that the magnetic field is the same at all points inside the solenoid.

The strength of the magnetic field produced by a solenoid depends on the number of turns per unit length ($n$) and the current ($I$) flowing through it: $B \propto nI$.